Research articlesCreating skyrmions and skyrmioniums using oscillating perpendicular magnetic fields
Introduction
Non-trivial topologically protected spin textures, such as magnetic skyrmions, can be created in ferromagnetic nanostructures with different geometries [1], [2], [3], [4], [5], [6], [7]. Magnetic skyrmions are characterized by the topological charge Q. For skyrmions with polarity p = +1, i.e., magnetization at the center in the +z direction, the topological charge is Q = 1, and for skyrmions with polarity p = −1, the topological charge is Q = −1 [6], [8].
The topological protection of magnetic skyrmions allows them to evade obstacles or defects in the nanostructures as they move [9], and also coexist in the form of clusters, without mutual annihilation [10]. Magnetic skyrmions can be moved with small current densities [8], reducing the undesirable Joule heating that is detrimental in Spintronics applications, e.g., racetrack memories [11].
Skyrmioniums, also called target skyrmions [12] or 2-skyrmions [13], are another type of spin texture similar to skyrmions, that can also be created in ferromagnetic nanostructures [14], [15], [16], [12], [17], [18]. A skyrmionium can be considered as a combination of two skyrmions with opposite topological charge [17], [12], resulting in a total topological charge Q = 0. This allows the skyrmionium, unlike the skyrmion, to move without suffering deflections due to the skyrmion Hall effect (SkHE). This property is essential to read and write information in potential applications of skyrmioniums as components of devices for magnetic recording [18].
Skyrmioniums can reach higher velocities in comparison with a skyrmion [19], [17], another property that is relevant for applications in Spintronics.
Skyrmioniums in magnetic nanostructures arise in micromagnetic simulations [20], [15], [21] and have been experimentally observed at low temperature and room temperature [12], [22], [23], [24]. They can be created in ferromagnetic nanostructures by tuning parameters such as the ratio of the thickness to the radius of the nanodisk, perpendicular magnetic anisotropy, and Dzyaloshinskii-Moriya interaction [20], or using an external perturbation, e.g., spin polarized current [15], and static perpendicular magnetic field [25], [14], [12].
However, it is necessary to look for methods that allow us to have selectivity in creating either magnetic skyrmions, or skyrmioniums, in an isolated nanostructure.
In the present work, we propose a simple method to create selectively these textures, in a nanodisk with a perpendicularly magnetized single-domain, using oscillating perpendicular magnetic fields with frequencies equal to the frequencies of the spin wave modes of these textures. To demonstrate this idea, we used the open source code Mumax3 [26], with a cell size 1 1 L nm3, where L is the thickness of the nanodisk. We assumed T = 0 K, however, the present method is valid at room temperature (see Supplementary material). The material used was Cobalt with parameters [20], [27]: saturation magnetization = 5.8 A/m, exchange stiffness = 15 pJ/m, perpendicular uniaxial anisotropy constant = 0.8 and 1.0 MJ/m3, and Dzyaloshinskii-Moriya exchange constant ranging between 3.4 and 4.0 mJ/m2.
Section snippets
Results and discussion
We have simulated a thin Cobalt nanodisk deposited on a Pt substrate (Co/Pt), with diameter D = 150 nm and thickness L = 1 nm.
First, in order to obtain the relaxed magnetic state of the nanodisk, we have considered in our micromagnetic simulations three initial magnetic configurations: perpendicular single domain, skyrmion, and skyrmionium. The energies of the relaxed states are shown in Fig. 1. These were obtained using a large damping constant of = 0.3 for faster convergence. For all our
Conclusions
In summary, in this work, we have studied the formation of a skyrmion and a skyrmionium in a Co/Pt nanodisk using micromagnetic simulations. Our results show that a perpendicular oscillating magnetic field can be used to create a skyrmion or a skyrmionium, when the frequency of the magnetic fields is equal to the frequencies of the spin wave modes, and the duration of the pulse is in the sub nanosecond time range.
We have also shown that the process of formation of skyrmions and skyrmioniums is
CRediT authorship contribution statement
H. Vigo-Cotrina: Conceptualization, Methodology, Software, Writing - original draft. A.P. Guimarães: Supervision, Writing - review & editing, Resources.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
The authors would like to thank the support of the Brazilian agencies FAPERJ and CNPq.
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2022, Physics Letters, Section A: General, Atomic and Solid State PhysicsCitation Excerpt :In addition, the scientists found a novel skyrmion named skyrmionium, also known as 2π-vortex or target skyrmion [26,27], which had the characteristic of zero topological number, and as a result, the movement of skyrmionium would not be influenced by SkHE in a racetrack [28–33]. At present, many researchers are committed to the research of forming and driving skyrmionium [34–40]. Most of them use spin polarized current to manipulate skyrmionium.
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2020, Journal of Magnetism and Magnetic MaterialsCitation Excerpt :Unlike the skyrmion, the spatial profile of a skyrmionium has an additional outer out-of-plane domain. This domain has the same direction of the magnetization of the core [13–18]. Therefore, a skyrmionium can be considered a combination of two skyrmions with opposite topological charges (Q = +1 and Q = −1), resulting in a total topological charge Q = 0 [16,22].
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